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Unless the stars comes so close that they actually collide, two stars will not be able to catch each other gravitationally. The reason is energy conservation: As they approach each other, their potential energy is converted into kinetic energy, increasing their velocities. When they are closest, their velocities are at their highest, but since there's ...


5

There are at least two interpretations to this problem: Per Wikipedia, Jupiter's surface gravity is $2.528$ times Earth's. Thus, if the Earth were $2.528$ times denser, it would have the same surface gravity as Jupiter. The Earth's current density is $5.514$ grams per cubic centimeter, so the new density would be $2.528 \times 5.514$, or about $13.9394$ ...


5

You only need two formulae. Gravitational field of a spherically symmetric mass distribution is given by $$g = \frac{GM}{R^2},$$ where $M$ is the mass inside a radius $R$. The second formula is the average density of a sphere is its mass divided by its volume, hence $$\rho = \frac{M}{(4/3)\pi R^3}$$ These two formulae can obviously be put together to give ...


2

It's called gravitational lensing. Here's a link to the wikipedia article on the subject: http://en.wikipedia.org/wiki/Gravitational_lens. Gravity affects everything, including light. A massive object such as a star, a galaxy, or in this case, a cluster of galaxies, bends the path of photons that pass very close to the massive object. Bending light is the ...


2

Is the SOI a spherical region or a oblate-spheroid-shaped region? The sphere of influence is neither a sphere nor an oblate spheroid. It is a surface with no name. An approximation of this surface is $$\left(\frac r R\right)^{10}(1+3\cos^2\theta) = \left( \frac m M \right)^4$$ This is neither a sphere nor an oblate spheroid, and this is but an ...



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